Difference between revisions of "Dickson polynomial"

Latest revision as of 18:41, 24 May 2016

The Dickson polynomials of the first kind are $$\left\{ \begin{array}{ll} D_0(x,\alpha) &=2 \\ D_n(x,\alpha) &=\displaystyle\sum_{k=0}^{\lfloor \frac{n}{2} \rfloor} \dfrac{n}{n-k} {{n-p} \choose p} (-\alpha)^p x^{n-2k}. \end{array} \right.$$

The Dickson polynomials of the second kind are $$\left\{ \begin{array}{ll} E_0(x,\alpha) &= 1 \\ E_n(x,\alpha) &= \displaystyle\sum_{k=0}^{\lfloor \frac{n}{2} \rfloor} {{n-k} \choose k} (-\alpha)^k x^{n-2k}. \end{array} \right.$$

Laguerre $L_n^{(\alpha)}$

Bateman $F_n$

Bernoulli $B$

Bessel poly

Chebyshev T

Chebyshev U

Dickson

Euler $E$

Gegenbauer $C$

Hermite (phys)

Hermite (prob)

Jacobi $P^{(\alpha,\beta)}$

Laguerre $L$

Legendre $P$

Bernoulli $B$

Chebyshev $T$

Fibonacci

Lucas